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MANAGING INVENTORIES OF CASH

William Baumol was the first to notice that this simple inventory model can tell us something about the management of cash balances.5 Suppose that you keep a reservoir of cash that is steadily drawn down to pay bills. When it runs out, you replenish the cash balance by selling short-term securities. In these circumstances your inventory of cash also follows a sawtoothed pattern like the pattern for inventories we saw in Figure 2.7. In other words, your cash management problem is just like the problem of finding the optimal order size faced by the builders` merchant. You simply need to redefine the variables. Instead of bricks per order, the order size is defined as the value of short-term securities that are sold whenever the cash balance is replenished. Total cash outflow takes the place of the total number of bricks sold. Cost per order becomes the cost per sale of securities, and the carrying cost is just the interest rate. Our formula for the amount of securities to be sold or, equivalently, the initial cash balance is therefore

Initial cash balance =_ 2_annual cash outflows_cost per sale of securities interest rate

The optimal amount of short-term securities sold to raise cash will be higher when annual cash outflows are higher and when the cost per sale of securities is higher. Conversely, the initial cash balance falls when the interest rate is higher.

The Optimal Cash Balance

Suppose that you can invest spare cash in U.S. Treasury bills at an interest rate of 8 percent, but every sale of bills costs you $20. Your firm pays out cash at a rate of $105,000 per month, or $1,260,000 per year. Our formula for the initial cash balance tells us that the optimal amount of Treasury bills that you should sell at one time is

_2 1,260,000 20 = $25,100 .08

Thus your firm would sell approximately $25,000 of Treasury bills four times a month about once a week. Its average cash balance will be $25,000/2, or $12,500.

In Baumol`s model a higher interest rate implies smaller sales of bills. In other words, when interest rates are high, you should hold more of your funds in interestbearing securities and make small sales of these securities when you need the cash. On the other hand, if you use up cash at a high rate or there are high costs to selling securities, you want to hold large average cash balances. Think about that for a moment. You can hold too little cash. Many financial managers point with pride to the extra interest

that they have earned. Such benefits are highly visible. The costs are less visible but they can be very large. When you allow for the time that the manager spends in monitoring the cash balance, it may make some sense to forgo some of that extra interest.